Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data
In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd Weibull Lomax, Weibull-Lomax, Marshall-Olkin alpha power e...
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| Format: | Article |
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MDPI AG
2022-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/20/10431 |
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| author | Salem A. Alyami Ibrahim Elbatal Naif Alotaibi Ehab M. Almetwally Hassan M. Okasha Mohammed Elgarhy |
| author_facet | Salem A. Alyami Ibrahim Elbatal Naif Alotaibi Ehab M. Almetwally Hassan M. Okasha Mohammed Elgarhy |
| author_sort | Salem A. Alyami |
| collection | DOAJ |
| description | In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd Weibull Lomax, Weibull-Lomax, Marshall-Olkin alpha power extended Weibull and exponentiated generalized alpha power exponential distributions, etc. The suggested model includes the Topp-Leone Weibull, Topp-Leone Linear failure rate, Topp-Leone exponential and Topp-Leone Rayleigh distributions as a special case. Several characteristics of the new suggested model including quantile function, moments, moment generating function, central moments, mean, variance, coefficient of skewness, coefficient of kurtosis, incomplete moments, the mean residual life and the mean inactive time are derived. The probability density function of the Topp–Leone modified Weibull distribution can be right skewed and uni-modal shaped but, the hazard rate function may be decreasing, increasing, J-shaped, U-shaped and bathtub on its parameters. Three different methods of estimation as; maximum likelihood, maximum product spacing and Bayesian methods are used to estimate the model parameters. For illustrative reasons, applications of the Topp–Leone modified Weibull model to four real data sets related to medical and engineering sciences are provided and contrasted with the fit reached by several other well-known distributions. |
| first_indexed | 2024-03-09T20:46:58Z |
| format | Article |
| id | doaj.art-ad4a5065619e4b888608bb0ac87b5f13 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T20:46:58Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-ad4a5065619e4b888608bb0ac87b5f132023-11-23T22:44:32ZengMDPI AGApplied Sciences2076-34172022-10-0112201043110.3390/app122010431Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering DataSalem A. Alyami0Ibrahim Elbatal1Naif Alotaibi2Ehab M. Almetwally3Hassan M. Okasha4Mohammed Elgarhy5Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaFaculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, EgyptDepartment of Statistics, Faculty of Science, King AbdulAziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThe Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, EgyptIn this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd Weibull Lomax, Weibull-Lomax, Marshall-Olkin alpha power extended Weibull and exponentiated generalized alpha power exponential distributions, etc. The suggested model includes the Topp-Leone Weibull, Topp-Leone Linear failure rate, Topp-Leone exponential and Topp-Leone Rayleigh distributions as a special case. Several characteristics of the new suggested model including quantile function, moments, moment generating function, central moments, mean, variance, coefficient of skewness, coefficient of kurtosis, incomplete moments, the mean residual life and the mean inactive time are derived. The probability density function of the Topp–Leone modified Weibull distribution can be right skewed and uni-modal shaped but, the hazard rate function may be decreasing, increasing, J-shaped, U-shaped and bathtub on its parameters. Three different methods of estimation as; maximum likelihood, maximum product spacing and Bayesian methods are used to estimate the model parameters. For illustrative reasons, applications of the Topp–Leone modified Weibull model to four real data sets related to medical and engineering sciences are provided and contrasted with the fit reached by several other well-known distributions.https://www.mdpi.com/2076-3417/12/20/10431Topp–Leone distributionmodified Weibull distributionmomentsmoment generating functionmaximum likelihood approachmaximum product spacing approach |
| spellingShingle | Salem A. Alyami Ibrahim Elbatal Naif Alotaibi Ehab M. Almetwally Hassan M. Okasha Mohammed Elgarhy Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data Applied Sciences Topp–Leone distribution modified Weibull distribution moments moment generating function maximum likelihood approach maximum product spacing approach |
| title | Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data |
| title_full | Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data |
| title_fullStr | Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data |
| title_full_unstemmed | Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data |
| title_short | Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data |
| title_sort | topp leone modified weibull model theory and applications to medical and engineering data |
| topic | Topp–Leone distribution modified Weibull distribution moments moment generating function maximum likelihood approach maximum product spacing approach |
| url | https://www.mdpi.com/2076-3417/12/20/10431 |
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